Problem: Rewrite as a simplified fraction. ${1.\overline{75} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 175.7575...\\ 1x &= 1.7575...\end{align*}}$ Subtracting the two equations, we have: ${99x = 174}$ ${x = \dfrac{174}{99}} $ ${x = \dfrac{58}{33}} \text{or} {1 \dfrac{25}{33}}$